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[Mon Jul 28 12:38:54 2003]
If all is OK, then all values should be 1.23607 (or approximately so depending on the decimal places you have specified for your results).
Ako je sve u redu, tada bi sve vrijednosti trebale biti 1.23607 (ili približno tomu, ovisno o decimalnim mjestima koja smo odredili za naše rezultate).
[Mon Jul 28 12:38:54 2003]
Having performed this test satisfactorily, replace x(0) by 1.25 once again and then experimentation can begin
Ako je ovaj test zadovoljavajuće riješen, zamijenite x0 s 1.25 još jednom i tada eksperimentiranje može započeti
[Mon Jul 28 12:40:51 2003]
Let us consider first the lower equilibrium point, x*1 = - 3.23607 and an initial value of x(0) = -3.5.
Razmotrimo prvo nižu točku ravnoteže, x* 1 = - 3.23607 i početnu vrijednost x(0) = - 3.5.
[Mon Jul 28 12:40:51 2003]
Given this initial value, the system declines very rapidly
S obzirom na ovu početnu vrijednost, sustav opada vrlo brzo
[Mon Jul 28 12:42:08 2003]
moving further in the negative direction.
odmičući se u negativnom smjeru.
[Mon Jul 28 12:42:20 2003]
What about a value slightly larger than -3.2?
Što je s vrijednosti malo većom od - 3.2?
[Mon Jul 28 12:42:33 2003]
Consider the value
Razmorimo vrijednost
[Mon Jul 28 12:44:03 2003]
The system certainly moves away from the fixed point, but then begins to oscillate between the values 0 and 2.
Sustav se svakako odmiče od fiksne točke, ali tada počinje oscilirati između vrijednosti 0 i 2.
[Mon Jul 28 12:46:31 2003]
For the moment we shall not concern ourselves with the oscillatory behaviour, and we shall take up this point later.
Zasad se nećemo baviti oscilatornim ponašanjem, već ćemo se ovim problemom pozabaviti kasnije.
[Mon Jul 28 12:46:41 2003]
All we are establishing here is that for initial values a little larger than -3.23607 the system moves away from it, which it certainly does.
Sve što ovdje utvrđujemo jest da ako su početne vrijednosti malo veće od - 3.23607 sustav se odmiče od njih, što je svakako točno.
[Mon Jul 28 12:47:04 2003]
Hence, the fixed point x*1 = -3.23607 is locally unstable.
Stoga, fiksna točka x* 1 = - 3.23607 je lokalno nestabilna.
[Mon Jul 28 12:47:13 2003]
What about the fixed point x*2 = 1.23607?
Što je s fiksnom točkom x* 2 = 1.23607?
[Mon Jul 28 12:47:57 2003]
Consider first a value 0.9.
Razmorimo prvo vrijednost 0.9.
[Mon Jul 28 12:48:19 2003]
Very soon the system settles into an oscillatory behaviour, oscillating once again between 0 and 2.
Vrlo brzo sustav se počinje oscilatorno ponašati, oscilirajući ponovo između 0 i 2.
[Mon Jul 28 12:48:47 2003]
Consider an initial point above x*2 = 1.23607, say 1.5.
Razmorimo početnu točku iznad x* 2 = 1.23607, recimo 1.5.
[Mon Jul 28 12:48:53 2003]
The system once again converges on the oscillation between 0 and 2.
Sustav se još jednom spaja na oscilaciji između 0 i 2.
[Mon Jul 28 12:48:53 2003]
What if we
Što ako bismo
[Mon Jul 28 12:54:30 2003]
choose values even closer to the fixed point?
izabrali vrijednosti koje su još bliže fiksnoj točki?
[Mon Jul 28 12:55:53 2003]
Consider values 1.2 and 1.25, respectively.
Razmotrimo vrijednosti 1.2 i 1.25, zasebno.
[Mon Jul 28 12:57:13 2003]
The fixed point x*2 = 1.23607 is neither an attractor nor a repellor
Fiksna točka x* 2 = 1.23607 nije niti atraktor niti repelor
[Mon Jul 28 12:59:40 2003]
The same equilibrium points have once again been established.
Ponovno su uspostavljene iste točke ravnoteže.
[Mon Jul 28 13:00:09 2003]
The phase diagram representation of the problem is drawn in figure 1.8.
Prikaz problema pomoću faznog dijagrama je upisan u sliku 1.8.
[Mon Jul 28 13:00:44 2003]
The curve represents the equation 2 - 1/2x2(t) -x(t).
Krivulja predstavlja jednadžbu 2 - 1/2x2(t) -x(t).
[Mon Jul 28 13:00:57 2003]
Here we are treating the curve as continuous.
Ovdje krivulju smatramo neprekidnom.
[Mon Jul 28 14:05:45 2003]
This is important.
To je važno.
[Mon Jul 28 14:07:07 2003]
To the left of x*2 = - 3.23607 ?x(t1) < 0, which indicates that x(t) is falling, so the system is moving even further in the negative direction.
xt1 0, koji ukazuje da xt pada, tako da se sustav pomiče još dalje u negativnom smjeru.
[Mon Jul 28 14:07:18 2003]
Slightly to the right of x*2 = -3.23607 then ?x(t + I) > 0 and so x(t) is rising, i.e.
Malo udesno od x* 2 = 3.23607 tada?xt (+ Ja) 0 i tako xt raste, tj.
[Mon Jul 28 14:07:34 2003]
moving away from the fixed point.
odmiče se od fiksne točke.
[Mon Jul 28 14:07:54 2003]
From this perspective the fixed point
Iz ove perspektive fiksna točka
[Mon Jul 28 14:11:30 2003]
Now turn to the larger of the fixed points, x*1 = 1.23607.
Sada pogledajmo veću fiksnu točku, x* 1 = 1.23607.
[Mon Jul 28 14:11:53 2003]
Slightly to the left of this fixed point, in its neighbourhood, ?x(t+ 1) > 0 and so x(t) is rising.
Malo ulijevo od ove fiksne točke, u njenoj okolini,?xt (+ 1) 0 tako da xt raste.
[Mon Jul 28 14:13:06 2003]
Slightly to the right of the fixed point, ?x(t+ 1) < 0 and so x(t) is falling.
Malo udesno od fiksne točke,?xt (+ 1) 0 tako da xt pada.
[Mon Jul 28 14:14:31 2003]
In terms of this continuous representation it appears that the fixed point x*2 = 1.23607 is locally stable and is an attractor.
U smislu ovog neprekidnog prikaza čini se da je fiksna točka x* 2 = 1.23607 lokalno stabilna i da je atraktor.
[Mon Jul 28 14:14:46 2003]
But this seems in contradiction to our spreadsheet investigation - at least for the higher fixed point!
Ali to je u kontradikciji s našim ispitivanjem proračunske tablice - barem što se tiče više fiksne točke!
[Mon Jul 28 14:14:46 2003]
Why is this?
Zbog čega je tako?
[Mon Jul 28 14:20:10 2003]
What has been illustrated here is that the properties of continuous models are not necessarily the same for their discrete counterpart.
Ovdje smo prikazali kako svojstva kontinuiranih modela nisu nužno jednaka i za njihove pojedinačne protuparove.
[Mon Jul 28 14:20:41 2003]
In fact, for many discrete nonlinear models oscillatory behaviour arises.
Ustvari, kod mnogih pojedinačnih nelinearnih modela dolazi do oscilatornog ponašanja.
[Mon Jul 28 14:23:10 2003]
We shall see why in later chapters.
Zašto je tako, vidjet ćemo u narednim poglavljima.
[Mon Jul 28 14:24:36 2003]
For the present all we wish to do is point out that if you are interested in continuous models, then the difference representation of the model with its accompanying phase line is sufficient to establish fixed points and their local stability or instability.
Zasad samo želimo istaknuti da ako ste zainteresirani za kontinuirane modele, tada je prikaz razlika modela s njegovom pratećom faznom linijom dovoljan za uspostavljanje fiksnih točaka i njihove lokalne stabilnosti ili nestabilnosti.
[Mon Jul 28 14:24:36 2003]
If, however, the model is in discrete time, then it should be investigated on a spreadsheet to establish whether some of the fixed points exhibit oscillations
Ako je, međutim, model u zasebnom vrjemenu, tada bi trebao biti ispitivan na proračunskoj tablici kako bi se utvrdilo da li neka od fiksnih točaka ispoljava oscilacije
[Mon Jul 28 14:26:00 2003]
Let us take one further example to illustrate these points.
Uzmimo još jedan primjer kako bismo ilustrirali ove točke.
[Mon Jul 28 14:26:00 2003]
Consider the nonlinear recursive model
Razmotrimo nelinearni rekurzivni model
[Mon Jul 28 14:26:31 2003]
The difference form of the model is
Diferencijalna forma modela je
[Mon Jul 28 14:28:03 2003]
Since the difference equation is to the power three, then there are three solutions to this equation.
S obzirom da diferencijalna jednadžba iam potenciju tri, tada postoje tri rješenja ove jednadžbe.
[Mon Jul 28 14:29:35 2003]
The reason why two fixed points are the same is clearly shown in figure 1.9, which plots the equation
Razlog zbog kojega su dvije fiksne točke jednake jasno je prikazan na slici 1.9, koja grafički prikazuje jednadžbu
[Mon Jul 28 14:30:24 2003]
and shows the phase line below
i prikazuje faznu liniju ispod
[Mon Jul 28 14:31:07 2003]
Consider first the continuous form of the model as shown in figure 1.9.
Razmotrimo prvo kontinuirani oblik modela kako je prikazano na slici 1.9.
[Mon Jul 28 14:31:07 2003]
To the left of
Lijevo od
[Mon Jul 28 14:35:24 2003]
The unusual nature of the fixed point x* = 1 is shown by the phase line with its arrows.
Neobična priroda fiksne točke x* = 1 je prikazana faznom linijom sa svojim strelicama.
[Mon Jul 28 14:36:23 2003]
The arrows are moving towards the fixed point x* = 1 and then away from it to the right.
Strelice se kreću prema fiksnoj točki x* = 1 a zatim dalje od nje na desno.
[Mon Jul 28 14:37:16 2003]
It is as if the system is being 'shunted along'.
Kao da je sustav 'preusmjeren dalje'.
[Mon Jul 28 14:37:16 2003]
For this reason, the fixed point x* = 1 is referred to as a shunt
Iz tog razloga, fiksna točka x* = 1 se naziva skretnicom
[Mon Jul 28 14:40:27 2003]
Does the discrete form of the model reveal these properties?
Da li zaseban oblik modela otkriva ova svojstva?
[Mon Jul 28 14:41:47 2003]
In setting up the model on a spreadsheet simply enter the initial value for the variable x, and then in the cell immediately below the initial value, type in the formula - moving the cursor to the cell above when placing in the variable x.
Pri stavljanju modela u proračunsku tablicu, jednostavno unesemo početnu vrijednost za varijablu x, i tada u ćeliju neposredno ispod početne vrijednosti, upišemo formulu - pomičući kursor na ćeliju iznad kada upisujemo varijablu x.
[Mon Jul 28 14:42:03 2003]
Then copy this cell to the clipboard and paste down for as many periods as you wish.
Zatim kopiramo ovu ćeliju na "clipboard" i lijepimo je dalje za onoliko perioda razdoblja koliko želimo.
[Mon Jul 28 14:42:35 2003]
Doing this reveals the following.
To otkriva sljedeće.
[Mon Jul 28 14:43:10 2003]
A value to the left of - 1, say -1.2, leads the system ever more in the negative direction.
Vrijednost lijevo od 1, recimo 1.2, vodi sustav sve dalje u negativnom smjeru.
[Mon Jul 28 14:44:08 2003]
A value just above - 1, say -0.9, leads the system towards the upper fixed point x* = 1.
Vrijednosni netom iznad - 1, recimo - 0.9, vodi sustav prema gornjoj fiksnoj točki x* = 1.
[Mon Jul 28 14:45:13 2003]
Taking a value just to the left of the upper fixed point, say 0.5, leads the system to the fixed point x* = 1.
Uzimanje vrijednosti samo lijevo od gornje fiksne točke, recimo 0.5, vodi sustav prema fiksnoj točki x* = 1.
[Mon Jul 28 14:45:48 2003]
Taking a value just above this fixed point, say 1.1, soon leads the system into ever-higher values.
Uzimanje vrijednosti samo povrh ove fiksne točke, recimo 1.1, uskoro dovodi sustav do sve većih vrijednosti.
[Mon Jul 28 14:46:55 2003]
Once again we have verified the same properties for this specific model.
Još jednom smo potvrdili ista svojstva za ovaj konkretan model.
[Mon Jul 28 14:48:58 2003]
In particular, we have illustrated that the lower fixed point is a repellor, and is locally unstable, while the upper fixed point (strictly two) is a shunt.
Poglavito, pokazali smo da je niža fiksna točka repelor, i da je lokalno nestabilna, dok je gornja fiksna točka (isključivo dva) skretnica.
[Mon Jul 28 14:48:58 2003]
In this particular example, therefore, there is no disparity in the conclusions drawn between the continuous form of the model and the discrete form
U ovom konkretnom primjeru, stoga, nema razlika u zaključcima izvedenima iz kontinuiranog oblika modela i onih iz zasebnog oblika
[Mon Jul 28 14:51:58 2003]
We need to be more precise about continuous models and how to represent them.
Moramo biti precizniji kada govorimo o kontinuiranim modelima i kako ih predstavljamo.
[Mon Jul 28 14:52:25 2003]
This is the purpose of this section.
To je svrha ovog odlomka.
[Mon Jul 28 14:53:11 2003]
In section 1.10 we shall consider a spreadsheet representation of continuous models using Euler's approximation.
10 razmotrit ćemo tablični prikaz kontinuiranih modela pomoću Eulerove aproksimacije.
[Mon Jul 28 14:53:11 2003]
This will be found especially useful when we consider systems of equations in chapter 4 and later
To će biti naročito korisno kada budemo razmatrali sustave jednadžbi u poglavlju 4 i kasnije
[Mon Jul 28 14:57:14 2003]
If I does not enter explicitly as a separate variable, then the differential equation is said to be an autonomous differential equation
Ako I ne ulazim izričito kao zasebna varijabla, onda se takva diferencijalna jednadžba naziva autonomnom diferencijalnom jednadžbom
[Mon Jul 28 14:59:05 2003]
This is the mathematicians' use of the word 'autonomous'.
Ovo je matematička upotrijeba riječi 'autonoman'.
[Mon Jul 28 15:00:05 2003]
They mean independent of time.
Pod tim se podrazumijeva neovisnost o vremenu.
[Mon Jul 28 15:00:05 2003]
When an economist refers to a variable being autonomous they mean being independent of income
Kada ekonomist govori o na autonomnoj varijabli, on hoće reći da je ona neovisna o prihodu
[Mon Jul 28 15:02:32 2003]
then this is a first-order differential equation.
tada je to diferencijalna jednadžba prvog reda.
[Mon Jul 28 15:03:12 2003]
dx(t)/dt simply denotes the change in x(t) over time, and 4 - 2x(t) gives the formula for this change.
dx(t)/dt jednostavno označava promjenu x(t) tijekom vremena, a 4 - 2x(t) predstavlja formulu za ovu promjenu.
[Mon Jul 28 15:03:38 2003]
Since time does not enter explicitly in this equation then it is autonomous.
Budući da vrijeme ne ulazi eksplicitno u ovu jednadžbu, znači da je autonomna.
[Mon Jul 28 15:03:38 2003]
A non-autonomous equation would be something like
Ne-autonomna jednadžba bila bi nešto poput
[Mon Jul 28 15:06:16 2003]
In this book we shall consider only autonomous differential equations as defined here.
U ovoj knjizi ćemo razmatrati samo autonomne diferencijalne jednadžbe kako su ovdje definirane.
[Mon Jul 28 15:06:16 2003]
Since x is always assumed to be a function of t, then we can drop the time designation and write ( 1.19) more succinctly as
Pošto se uvijek pretpostavlja da je x funkcija od t, tada možemo izbaciti oznaku vremena i pisati (1.19) jezgrovitije kao
[Mon Jul 28 15:08:05 2003]
A convention used in mathematics, and one we shall use too, is to denote dx/dt by the dot-symbol, i.e.
Običaj koji se koristi u matematici, i koji ćemo mi također koristiti, je označiti dx/dt simbolom točke, tj.
[Mon Jul 28 15:08:24 2003]
This now means that (1.21) can be written as
To sada znači da (1.21) možemo pisati kao
[Mon Jul 28 15:09:43 2003]
The fixed point, the equilibrium point, of this model is where x is unchanging, which means where x = 0.
Fiksna točka, točka ravnoteže, ovog modela je tamo gdje je x nepromjenjiv, što znači tamo gdje je x = 0.
[Mon Jul 28 15:09:43 2003]
This gives the fixed point
To daje fiksnu točku
[Mon Jul 28 15:10:58 2003]
Furthermore, this fixed point is globally stable.
Nadalje, ta fiksna točka je općenito stabilna.
[Mon Jul 28 15:11:18 2003]
We establish this in exactly the same way as we did with our discrete models.
To smo ustanovili na sasvim isti način kao s našim diskretnim modelima.
[Mon Jul 28 15:11:18 2003]
The situation is shown in figure 1.10
Situacija je izložena na slici 1.10
[Mon Jul 28 15:13:53 2003]
The model has only one fixed point, namely x* = 2.
Model ima samo jednu fiksnu točku, i to x* = 2.
[Mon Jul 28 15:14:53 2003]
The relationship between the change in x, denoted x, and the variable x is shown in the upper diagram in figure 1.10.
Veza između promjene u x, označenog x, i varijable x prikazana je u gornjem dijagramu na slici 1.10.
[Mon Jul 28 15:15:23 2003]
Given x(0) for period 0, the initial period, where we assume x(0) < 2, then x > 0 and so x is rising.
Ako je x0 za razdoblje 0, početni period, gdje pretpostavljamo da je x0 2, tada je x 0 tako da x raste.
[Mon Jul 28 15:16:40 2003]
For any initial point above x* = 2, then x < 0 and so x is falling.
Za bilo koju početnu točku iznad x* = 2, tada je x 0 tako da x pada.
[Mon Jul 28 15:16:57 2003]
This is true no matter what value of x we take on the real line (other than the equilibrium point itself).
To vrijedi bez obzira koju vrijednost od x uzmemo na realnoj liniji (osim same točke ravnoteže).
[Mon Jul 28 15:17:08 2003]
Hence, x* = 2 is an attractor and is globally stable.
Stoga, x* = 2 je atraktor i općenito je stabilan.
[Mon Jul 28 15:17:08 2003]
If the model includes the initial condition, then
Ako model uključuje početni uvjet, tada
[Mon Jul 28 15:20:00 2003]
If f(x) is linear and negatively sloped, then there is a unique fixed point which is globally stable.
Ako je f(x) linearan i negativno nagnut, tada postoji jedinstvena fiksna točka koja je globalno stabilna.
[Mon Jul 28 15:21:48 2003]
If f(x) is linear and positively sloped, then there is a unique fixed point which is globally unstable.
Ako je f(x) linearan i pozitivno nagnut, tada postoji jedinstvena fiksna točka koja je općenito nestabilna.
[Mon Jul 28 15:22:05 2003]
If f(x) is nonlinear and more than one equilibrium exists, then we can refer only to local stability or instability in just the same way as we did with the discrete models earlier in this chapter.
Ako je f(x) nelinearan i ako postoji više od jedne ravnoteže, tada možemo govoriti samo o lokalnoj stabilnosti ili nestabilnosti na isti način kako smo činili s diskretnim modelima ranije u ovom poglavlju.
[Mon Jul 28 15:22:26 2003]
Return to the example of the shunt.
Vratimo se na primjer skretnice.
[Mon Jul 28 15:22:26 2003]
In its continuous form, we have the model
U svom kontinuiranom obliku, imamo model
[Mon Jul 28 15:25:19 2003]
where x is a continuous function of time.
gdje je x kontinuirana funkcija vremena.
[Mon Jul 28 15:25:28 2003]
The model is the same as that shown in figure 1.9 with the one exception that we place x on the vertical axis and not ?x(t + 1).
Model je isti kao onaj prikazan na slici 1.9 s tom razlikom iznimkom da stavljamo x na okomitu os a ne ?xt (+ 1).
[Mon Jul 28 15:25:28 2003]
All the remaining dynamics is the same
Sva preostala dinamika je jednaka
[Mon Jul 28 15:26:33 2003]
Continuous differential equations on a spreadsheet
Kontinuirane diferencijalne jednadžbe na proračunskoj tablici
[Mon Jul 28 15:27:11 2003]
Return to the simple example of section 1.9, with the initial condition
vratimo se na jednostavan primjer iz odlomka 1.9, s početnim uvjetom
[Mon Jul 28 15:29:02 2003]
Now this is a simple differential equation and there are known techniques for solving it.3 We are not concerned about that here, and we shall simply state that the solution is
Ovo je jednostavna diferencijalna jednadžba i postoje znane tehnike za njeno rješavanje ono.3 Nas to ovdje ne zanima, i jednostavno ćemo prikazati da je rješenje
[Mon Jul 28 15:31:16 2003]
Of course if we did know this we could plot the path of x(t) for some length of time.
Naravno, da smo to znali mogli bismo grafički prikazati putanju x(t) za neku veličinu vremena.
[Mon Jul 28 15:32:17 2003]
This is illustrated in figure 1.11.
To je ilustrirano na slici 1.11.
[Mon Jul 28 15:32:50 2003]
The solution curve x(t) goes through the point x(0) = 1, which is our initial condition, and shown by point P.
Krivulja rješenja x(t) prolazi kroz točku x0 = 1, što je naš početni uvjet, i prikazan je točkom P.
[Mon Jul 28 15:33:34 2003]
Now let an interval of time pass, which we shall denote by ?t.
Sada pustimo da prođe vremenski razmak, koji ćemo obilježiti kao ?t.
[Mon Jul 28 15:33:44 2003]
If we did know the solution curve, then at a value of t = 0.01, i.e.
Kad bismo znali krivulju rješenja, tada bi pri vrijednosti t = 0.01, tj.
[Mon Jul 28 15:35:00 2003]
This is shown by point Q.
To je prikazano točkom Q.
[Mon Jul 28 15:35:09 2003]
But suppose we do not know the solution curve.
Ali pretpostavimo da ne znamo krivulju rješenja.
[Mon Jul 28 15:35:13 2003]
Can we find an approximate value for point Q?
Možemo li naći približnu vrijednost za točku Q?
[Mon Jul 28 15:35:20 2003]
Yes, we can.
Da, možemo.
[Mon Jul 28 15:35:20 2003]
The change in x over
Promjena u x tijekom
[Mon Jul 28 15:38:50 2003]
time is the slope of the solution curve at any particular point.
vrijeme je nagib krivulje rješenja u bilo kojoj određenoj točki.
[Mon Jul 28 15:39:31 2003]
Consequently, the slope of the solution curve when t = 0 is 4 - 2( 1) = 2, since x(0) = 1.
Dakle, nagib krivulje rješenja kada je t = 0 iznosi 4 2 (1) = 2, jer je x0 = 1.
[Mon Jul 28 15:39:33 2003]
Then the value Q is approximated by x(1), and shown by the point R.
Tada je vrijednost Q približno određena pomoću x1, i prkazana točkom R.
[Mon Jul 28 15:41:51 2003]
which is not a bad approximation.
što nije loša procjena.
[Mon Jul 28 15:42:02 2003]
In fact, we can always improve on the approximation by taking smaller intervals of time.
Zapravo, možemo uvijek poboljšati procjenu uzimajući manje vremenske razmake.
[Mon Jul 28 15:42:02 2003]
More generally, our approximation is
Općenitije, naša procjena je
[Mon Jul 28 15:44:29 2003]
which is Euler's approximation to a differential equation.
što je Eulerova aproksimacija za diferencijalnu jednadžbu.
[Mon Jul 28 15:44:29 2003]
This approximation can be used for any linear or nonlinear single-variable differential equation
Ova aproksimacija se može koristiti za bilo koju linearnu ili nelinearnu diferencijalnu jednadžbu s jednom varijablom
[Mon Jul 28 15:44:53 2003]
Solution path on a spreadsheet
Linija rješenja na proračunsku tablicu
[Mon Jul 28 15:47:51 2003]
The advantage of the Euler approximation is that it applies to any linear or nonlinear differential equation even if we cannot explicitly solve the model.
Prednost Eulerovoe aproksimacije je što se ona može primijeniti na bilo koju linearnu ili nelinearnu diferencijalnu jednadžbu, čak i ako ne možemo eksplicitno riješiti model.
[Mon Jul 28 15:48:18 2003]
Furthermore, it is in such a form that it can readily be set out on a spreadsheet.
Nadalje, ona ima takav oblik da se može lako postaviti na proračunsku tablicu.
[Mon Jul 28 15:50:21 2003]
Before we begin, notice the importance of the initial condition.
Prije nego započnemo, obratimo pažnju na važnost početnog uvjeta.
[Mon Jul 28 15:51:12 2003]
This sets the solution path to pass through this point and only one such solution path can go through the initial condition for autonomous differential equations - and these are the only types of differential equations we shall be dealing with.
To smješta liniju rješenja da prođe kroz tu točku i samo jedna takva linija rješenja može proći kroz početni uvjet za autonomne diferencijalne jednadžbe - a to je jedini tip diferencijalnih jednadžbi koji ćemo rješavati.
[Mon Jul 28 15:51:41 2003]
This gives us the value of x at time period 0.
To nam daje vrijednost od x pri vremenskom intervalu 0.
[Mon Jul 28 15:52:25 2003]
We label the time periods 0, I, 2, .
Vremenska razdoblja označavamo kao 0, 1, 2,.
[Mon Jul 28 15:52:36 2003]
The elapse of time, however
Protok vremena, međutim
[Mon Jul 28 15:54:13 2003]
We shall see in chapter 4 how it can be adapted for two-variable models
U poglavlju 4 ćemo vidjeti 4 kako se može prilagoditi za modele s dvije varijable
[Mon Jul 28 15:57:27 2003]
The spreadsheet representation of our example is shown in figure 1.12.
Tablični prikaz našeg primjera prikazan je na slici 1.12.
[Mon Jul 28 15:57:52 2003]
In cell D3 we have the label 'dt =' to represent the symbol ?t, and set this value equal to 0.01 in cell E3.
U ćeliju D3 imamo oznaku 'dt =' koja predstavlja simbol ?t, i postavlja tu vrijednost jednako 0.01 u ćeliju E3.
[Mon Jul 28 15:58:30 2003]
In cell B6 we place our initial value, x(0) = 1.
U ćeliju B6 upisujemo našu početnu vrijednost, x(0) = 1.
[Mon Jul 28 15:58:30 2003]
Given this value, and the interval of time, we can calculate x(1) in cell B7 as follows
S obzirom na ovu vrijednost, i vremenski interval, možemo izračunati x1 u ćeliji B7 kako slijedi
[Mon Jul 28 15:59:54 2003]
This is then copied to the clipboard and pasted down.
To zatim kopiramo na "clipboard" i zalijepimo.
[Mon Jul 28 15:59:55 2003]
Here we have t = 0, 1, .
Ovdje imamo t = 0, 1,.
[Mon Jul 28 16:01:16 2003]
To see how good the approximation is we have also included the computations for the true solution curve in column C, i.e.
Da bismo vidjeli koliko je aproksimacija točna, također smo uključili izračune za ispravnu krivulju rješenja u stupcu C, tj.
[Mon Jul 28 16:01:33 2003]
Again we place the initial condition in cell C6.
Ponovo stavljamo početni uvjet u ćeliju C6.
[Mon Jul 28 16:01:33 2003]
Cell C7 then has the formula
Ćelija C7 tada ima formulu
[Mon Jul 28 16:03:27 2003]
Notice that time t is given by A 7*$E$3.
Uočimo da je vrijeme t određeno s A 7*$E$3.
[Mon Jul 28 16:08:14 2003]
This cell is then copied to the clipboard and pasted down.
Ta ćelija je zatim kopirana na "clipboard" i zalijepljena.
[Mon Jul 28 16:09:35 2003]
There are other superior approximations available that are given in books on differential equations
Postoje i druge vrhunske aproksimacije koje se nalaze u knjigama o diferencijalnim jednadžbama
[Mon Jul 28 16:12:14 2003]
In this chapter we have defined dynamic models, particularly deterministic dynamic models.
U ovom poglavlju smo definirali dinamičke modele, osobito determinističke dinamičke modele.
[Mon Jul 28 16:13:11 2003]
It is not sufficient to demonstrate that a model has an equilibrium, a fixed point, it is also important to establish whether the fixed point is stable or not.
Nije dovoljno demonstrirati da model ima ravnotežu, fiksnu točku, također je važno utvrditi da li je fiksna točka stabilna ili ne.
[Mon Jul 28 16:13:11 2003]
By means of some simple examples we highlighted the concepts of global stability and global instability, at tractors and repellors and periodic cycles
Pomoću nekih jednostavnih primjera istaknuli smo pojmove globalne stabilnosti i globalne nestabilnosti, kod traktora i repelora te kod periodičnih ciklusa
[Mon Jul 28 16:15:08 2003]
Discrete dynamic models are recursive and can be represented in a number of ways.
Diskretni dinamički model su rekurzivni i mogu se prikazati na nekoliko načina.
[Mon Jul 28 16:15:40 2003]
In this chapter we represented such systems as cobwebs, as a difference equation model and in a spreadsheet.
U ovom poglavlju smo predstavili takve sustave kao mreže, kao model diferencijalnih jednadžbi i pomoću proračunskih tablica.
[Mon Jul 28 16:16:19 2003]
The spreadsheet representation of a dynamical model allows a considerable amount of experimentation to be undertaken.
Tablični prikaz dinamičnog modela omogućuje znatnu količinu eksperimentiranja.
[Mon Jul 28 16:17:45 2003]
The difference equation representation allows us to introduce the concept of the phase line.
Prikaz diferencijalne jednažbe dopušta nam da uvedemo koncept fazne linije.
[Mon Jul 28 16:19:15 2003]
We next considered two nonlinear dynamical models, highlighting the more complex and more diverse behaviour to which they can give rise.
Zatim smo razmotrili dva nelinearna dinamička modela, istaknuli složenije i raznolikije ponašanje koje mogu potaknuti.
[Mon Jul 28 16:19:15 2003]
Finally, we outlined continuous dynamic models of one variable, showing how the solution paths of such differential equations can be set up on a spreadsheet
Naposljetku, izložili smo kontinuirane dinamičke modele s jednom varijablom, pokazujući kako linije rješenja takvih diferencijalnih jednadžbi mogu biti prikazana u proračunskoj tablici
[Mon Jul 28 17:16:31 2003]
In order to see what is taking place let us consider the difference equation version of the model.
Da bismo vidjeli što se događa, razmotrimo verziju diferencijalne jednadžbe modela.
[Wed Jul 30 11:06:26 2003]
Mapping the stock and flow structure of a system involves important decisions about the boundary of the model.
Ucrtavanje strukture stoka i toka sustava uključuje važne odluke o granici modela.
[Wed Jul 30 11:06:56 2003]
In reality, flows of material, people, and money into a stock have to come from somewhere;
U stvarnosti, tokovi materijala, ljudi, i novca u stok moraju potječe od nekuda poteći;
[Wed Jul 30 11:10:43 2003]
the flows out have to go somewhere.
istjecanja moraju nekamo ići.
[Wed Jul 30 11:11:10 2003]
To keep your models manageable, you must truncate these chains using sources and sinks, represented in the stock and flow maps by "clouds";
Da biste održali svoje modele, morate sasjeći ove okove pomoću izvora i izljeva, koji su predstavljeni u mapama stoka i toka u obliku "oblaka";
[Wed Jul 30 11:14:40 2003]
Sources and sinks represent the stocks supplying material to or absorbing material from the modeled system.
Izvori i izljevi predstavljaju stokove koji donose materijal u modelirani sustav, ili koji upijaju materijal iz modeliranog sustava.
[Wed Jul 30 11:15:25 2003]
Sources and sinks are assumed to have infinite capacity and can never constrain the flows they support.
Pretpostavlja se da izvori i izljevi imaju beskrajan kapacitet i da nikada neće moći obuzdati tokove koje podržavaju.
[Wed Jul 30 11:17:38 2003]
In the real world, the stocks supplying or absorbing flows have finite capacity and do influence the flows.
U stvarnome svijetu, stokovi koji dovode ili upijaju tokove imaju ograničen kapacitet i utječu na tokove.
[Wed Jul 30 11:17:59 2003]
When you truncate a stock and flow chain with a cloud you are setting the boundary of the model-stocks and flows beyond this point are ignored;
Kada odsječete lanac stoka i toka pomoću oblaka, vi postavljate granicu modela stokova, a tokovi izvan ove točke se ignoriraju;
[Wed Jul 30 11:17:59 2003]
you exclude all possible feedbacks from or interactions with the stocks outside the boundary
vi isključujete sve moguće povratne informacije od ili interakcije sa stokovima izvan granice
[Wed Jul 30 11:19:35 2003]
As a modeler you must critically examine these boundary assumptions;
Kao modelator, morate kritički ispitati ove granične pretpostavke;
[Wed Jul 30 11:20:39 2003]
you must, in the words of Barry Richmond (1993, p. 132), "challenge the clouds."
vi morate, prema riječima Barrya Richmonda (1993, str. 132), "prkositi oblacima."
[Wed Jul 30 11:22:28 2003]
Is it appropriate for your purpose to exclude the stocks outside the boundary of the model?
Da li je primjereno za vaš cilj isključiti stokove koji su izvan granica modela?
[Wed Jul 30 11:23:30 2003]
What feedbacks ignored by your model might exist in the real world, and might they affect your policy recommendations?
Koje povratne informacije koje ste previdjeli u svom modelu mogu postojati u stvarnosti, i mogu utjecati na vaše strategijske preporuke?
[Wed Jul 30 11:24:59 2003]
Can the sources for the flows be depleted and constrain the inflow?
Mogu li se izvori tokova istrošiti i ograničiti pritjecanje?
[Wed Jul 30 11:24:59 2003]
Can the sinks be filled and block the outflows, backing up the system like a clogged drain?
Mogu li se izljevi napuniti i blokirati istjecanje, podupirući sustav poput začepljenog odvoda?
[Wed Jul 30 11:28:20 2003]
Consider the automobile industry.
Razmotrimo automobilsku industriju.
[Wed Jul 30 11:30:45 2003]
A stock and flow map for automobile production might begin with production starts, WIP inventory, production, finished inventory, and shipments (Figure 6-16).
Mapa stoka i toka za proizvodnju automobila mogla bi započeti s počecima proizvodnje, inventarom nedovršene proizvodnje, proizvodnjom, zalihama gotovih proizvoda, i otpremom (slika 6-16).
[Wed Jul 30 11:31:13 2003]
Drawing the map with a source for the production start flow presumes that the supply of parts is unlimited and can never
Crtanje mape s izvorom početnog toka proizvodnje pretpostavlja da je zaliha dijelova neograničena i da nikada neće
[Wed Jul 30 11:32:56 2003]
constrain the production start rate.
ograničiti stopu početne proizvodnje.
[Wed Jul 30 11:33:37 2003]
Likewise, because shipments flow to a sink, the modeler has assumed stocks of product in the hands of dealers and customers have no effect on shipments.
Isto tako, s obzirom da otprema teče prema izljevu, modelator pretpostavlja da stokovi proizvoda u rukama prodavača i kupaca nemaju učinak na otpremu.
[Wed Jul 30 11:33:46 2003]
In challenging the clouds you ask whether these assumptions are reasonable.
U prkošenju oblacima vi postavljate pitanje da li su ove pretpostavke razumne.
[Wed Jul 30 11:34:11 2003]
For the auto industry they are not.
Za automobilsku industriju nisu.
[Wed Jul 30 11:34:57 2003]
Production starts require the automaker to have an adequate stock of parts.
Počeci proizvodnje zahtijevaju da proizvođač automobila ima odgovarajući stok dijelova.
[Wed Jul 30 11:35:01 2003]
Yet parts stocks may easily be
Pa ipak, stokovi dijelova se lako mogu
[Wed Jul 30 11:37:24 2003]
Suppliers cannot respond instantly to changes in parts orders.
Dobavljači ne mogu odmah reagirati na promjene u narudžbama dijelova.
[Wed Jul 30 11:38:32 2003]
Large orders may outstrip supplier capacity, leading to shortages.
Velike narudžbe mogu premašiti kapacitet dobavljača, dovodeći do pomanjkanja.
[Wed Jul 30 11:39:09 2003]
A strike at a supplier may interrupt the flow of parts to the firm.
Udarac po dobavljaču bi mogao prekinuti priljev dijelova tvrtci.
[Wed Jul 30 11:41:53 2003]
At the other end, shipments of new cars to dealers depend on the size of dealer stocks.
S druge strane, otprema novih automobila prodavačima ovisi o veličini trgovačkih stokova.
[Wed Jul 30 11:43:02 2003]
Dealers generally try to maintain about 40 to 60 days of inventory on their lots;
Prodavači općenito pokušavaju zadržati otprilike 40 do 60 dana inventar u svojoj ponudi;
[Wed Jul 30 11:43:50 2003]
this is enough to provide good selection for consumers without carrying excessive and costly inventory.
to je dovoljno da pruži dobar izbor potrošačima bez prekomjernog i skupog inventara.
[Wed Jul 30 11:44:24 2003]
If stocks are low relative to their targets, dealers order more from the manufacturers;
Ako su stokovi nisko u odnosu na svoje mete, prodavači naručuju veće količine od proizvođača;
[Wed Jul 30 11:45:20 2003]
if stocks are high, they cut back.
ako su stokovi visoko, tada smanjuju narudžbe.
[Wed Jul 30 11:46:16 2003]
Figure 6-17 expands the model boundary to capture these effects.
Slika 6-17 proširuje granice modela kako bi obuhvatila ove učinke.
[Wed Jul 30 11:47:01 2003]
The model now represents three distinct organizational entities-suppliers, manufacturers, and dealers.
Model sada predstavlja tri različite organizacijske tvorevine - dobavljače, proizvođače, i prodavače.
[Wed Jul 30 11:47:25 2003]
The inventory of parts held by the manufacturer is now explicit.
Inventar dijelova koji se nalaze kod proizvođača je sada jasan.
[Wed Jul 30 11:47:49 2003]
The supplier has the same basic structure as the automaker:
Dobavljač ima istu temeljnu strukturu kao proizvođač automobila:
[Wed Jul 30 11:51:20 2003]
a stock of finished inventory and a stock of work in process.
stok zalihe gotovih proizvoda i stok nedovršenih proizvoda.
[Wed Jul 30 11:51:20 2003]
At the shipment end, manufacturer shipments no longer disappear into a sink but flow into dealer stocks, allowing you to model the purchase rate as a function of the dealer inventory and sales to customers
Pri okončanju otpreme, otprema proizvođača više ne nestaje u izljevu, već utječe u trgovačke stokove, omogućujući vam da oblikujete kupovni tečaj kao posao trgovačkog inventara i prodaje kupcima
[Wed Jul 30 11:54:06 2003]
Initial stock and flow map for the automobile industry, showing the model boundary
Uvodna mapa stoka i toka za automobilsku industriju, pokazujući granicu modela
[Wed Jul 30 11:54:06 2003]
The sources and sinks for the flows through the system are assumed to be infinite and can have no impact on the dynamics
Pretpostavlja se da su izvori i izljevi za protok kroz sustav beskrajni i i da ne mogu imati utjecaj na dinamiku
[Wed Jul 30 11:58:32 2003]
Production Starts
Počeci proizvodnje
[Wed Jul 30 11:59:42 2003]
Finished Inventory
Zalihe gotovih proizvoda
[Wed Jul 30 12:02:40 2003]
You could and should continue to challenge the boundary of the model.
Mogli biste i trebali biste nastaviti izazvati granicama modela.
[Wed Jul 30 12:03:37 2003]
The model now allows you to represent supplier order processing, inventory management, and delivery, including the possibility that suppliers can become a bottleneck and starve automobile production.
Model vam sada omogućuje da prikažete obradu narudžbe dobavljača, upravljanje zalihama, i dostava, uključujući mogućnost da dobavljači postanu usko grlo i da izgladne proizvodnju automobila.
[Wed Jul 30 12:03:56 2003]
But now the suppliers are assumed to have unlimited parts and raw materials availability.
Ali sada se pretpostavlja dobavljači raspolažu neograničenim dijelovima i sirovinama.
[Wed Jul 30 12:04:13 2003]
Is this appropriate?
Da li je to primjereno?
[Wed Jul 30 12:06:17 2003]
It depends on the model purpose.
To ovisi o svrsi modela.
[Wed Jul 30 12:07:52 2003]
You could continue to expand the model boundary by adding the suppliers to the suppliers, and their suppliers, and so on, until you reached the point where it is acceptable to assume that the supply of materials to the farthest upstream supplier is unlimited.
Mogli biste nastaviti proširivati granice modela dodajući dobavljača na dobavljačima, i njihove dobavljače, i tako dalje, dok ne dosegnete točku gdje se može pretpostaviti da je zaliha materijala do najdaljeg dobavljača neograničena.
[Wed Jul 30 12:07:52 2003]
Alternatively, you could represent the entire upstream supply chain by a single aggregate supplier stage
S druge strane, mogli biste prikazati cjelokupni uzvodni opskrbni lanac pomoću jedne skupne faze nabave
[Wed Jul 30 12:15:17 2003]
The map shown in Figure 6-17 also assumes that dealer sales flow into a sink so there is no feedback from the stock of cars on the road to purchases of new cars.
Mapa prikazana na slici 6-17 također pretpostavlja da prihodi od prodaje prodavača utječu u izljev, tako da nema povratne informacije od stoka automobila na cesti do kupovine novih automobila.
[Wed Jul 30 12:16:30 2003]
This is obviously a bad assumption:
Ovo je očito loša pretpostavka:
[Wed Jul 30 12:20:54 2003]
Sales of new cars depend on the number and age of the cars people already have relative to their needs.
Prihodi od prodaje novih automobila ovise o broju i starosti automobila koje ljudi već posjeduju prema svojim potrebama.
[Wed Jul 30 12:21:54 2003]
People who have just acquired a new car are unlikely to buy another for several years, until their loan is paid off, their lease expires, or their car is involved in an accident and must be replaced (see section 2.2).
Ljudi koji su upravo kupili novi automobil vjerojatno neće kupovati drugi kupiti u sljedećih nekoliko godina, dok ne otplate zajam, dok im ne istekne ugovor o najmu, ili ako im se automobil ne ošteti u prometnoj nesreći pa ga moraju zamijeniti (vidi odlomak 2.2).
[Wed Jul 30 12:22:13 2003]
Figure 6-18 expands the downstream end of the stock and flow map to include the stock of cars on the road.
Slika 6-18 proširuje silazni dio mape stoka i toka kako bi uključila stok automobila na cesti.
[Wed Jul 30 12:22:33 2003]
You can continue to challenge the model boundary.
Možete nastaviti izazvati granice modela.
[Wed Jul 30 12:23:09 2003]
What happens to the cars when they are scrapped?
Što se dogodi s automobilima kada budu odbačeni?
[Wed Jul 30 12:23:49 2003]
In the current map, they simply disappear.
Na trenutnoj mapi, oni jednostavno nestanu.
[Wed Jul 30 12:25:01 2003]
In reality, they don't.
U stvarnosti, odbačeni automobili ne nestaju.
[Wed Jul 30 12:25:45 2003]
In North America some 10 to 12 million vehicles are scrapped per year.
U Sjevernoj Americi nekih 10 do 12 milijuna vozila godišnje biva odbačeno.
[Wed Jul 30 12:25:45 2003]
Roughly 94% are shredded and the steel and some nonferrous metals are
Otprilike 94 % biva uništeno, a čelik i neki obojeni metali bivaju
[Wed Jul 30 12:29:38 2003]
recovered, one of the highest recycling fractions of any industry.
obnovljeni, što je jedan od najvećih reciklažnih dijelova bilo koje industrije.
[Wed Jul 30 12:32:01 2003]
However, some cars end up abandoned as dangerous eyesores on the side of the road.
Međutim, neki automobil bivaju napušetni poput ružne opasnosti pokraj ceste.
[Wed Jul 30 12:32:01 2003]
And much of the plastic, glass, and other nonmetal materials end up in landfills, constituting a significant source of pollution (more than two billion discarded tires, most sitting in huge piles across the country, have already accumulated in the US
I mnogo plastike, stakla, i drugih nemetala završi na skladištima otpada, tvoreći značajan izvor zagađenja (u SAD-u se već nakupilo više od dvije milijarde odbačenih autoguma, većina nabacana na goleme hrpe diljem zemlje,
[Wed Jul 30 12:36:40 2003]
Adding a supplier and dealer sector to the stock and flow chain for automobile production.
Dodavanje sektora dobavljača i prodavača lancu stoka i toka za proizvodnju automobila.
[Wed Jul 30 12:36:40 2003]
Rectangles with rounded corners denote the boundaries between different organizational entities and decisionmaking units
Pravokutnici sa zaobljen uglovima označavaju granice između različitih organizacijskih tvorevina i jedinica za donošenje odluka
[Wed Jul 30 12:39:03 2003]
Supplier Production Starts
Dobavljač Počeci Proizvodnje
[Wed Jul 30 12:39:32 2003]
Supplier WIP
Dobavljač nedovršene proizvodnje
[Wed Jul 30 12:40:01 2003]
Supplier Production
Nabavna proizvodnja
[Wed Jul 30 12:40:25 2003]
Supplier Inventory
Nabava inventara
[Wed Jul 30 12:40:37 2003]
Supplier Shipments
Nabava otpreme
[Wed Jul 30 12:40:39 2003]
Parts Inventory
Zalihe dijelova
[Wed Jul 30 12:40:48 2003]
Production Starts
Počeci proizvodnje
[Wed Jul 30 12:40:48 2003]
WIP
nedovršena proizvodnja
[Wed Jul 30 12:43:20 2003]
Finished Inventory
Zalihe gotovih proizvoda
[Wed Jul 30 12:43:22 2003]
Shipments
Otprema
[Wed Jul 30 12:43:37 2003]
Dealer Stocks
Trgovački stokovi
[Wed Jul 30 12:43:37 2003]
New Car Sales
Prodaja novih automobila
[Wed Jul 30 12:47:33 2003]
The boundary now includes the stock of cars on the road, which feeds back to influence sales of new cars
Granica sada uključuje stok automobila na cesti, koji raste i utječe na prodaju novih automobila
[Wed Jul 30 12:48:30 2003]
Dealer Stocks
Trgovački stokovi
[Wed Jul 30 12:48:32 2003]
New Car Sales
Prodaja novih automobila
[Wed Jul 30 12:48:34 2003]
Cars on the Road
Automobili na cesti
[Wed Jul 30 12:48:34 2003]
Scrap Rate
Stopa otpada
[Wed Jul 30 12:53:36 2003]
By the mid 1990s, as landfills filled and environmental awareness grew, pressure
Do sredine 1990s, kako su se skladišta otpada punila, a ekološka svijest rasla, rastao je pritisak
[Wed Jul 30 12:55:16 2003]
built to recycle more of the material in cars.
da se reciklira što više automobilskog materijala.
[Wed Jul 30 12:58:37 2003]
Germany debated a law that would require auto manufacturers to take back their old cars when people deregistered them.
Njemačka je raspravljala o zakonu koji bi zahtijevao od proizvođača automobila da dobiju natrag svoje stare automobile nakon što vlasnici odjave registraciju.
[Wed Jul 30 12:58:37 2003]
Pushed by these forces, the auto industry, first in Europe and then in the US, began to study ways to increase the recovery of parts and the recycling of materials from cars
Natjerani ovim prisilama, automobilska industrija, prvo u Europi a zatim u SAD-u, počela je proučavati načine da poveća povrat dijelova i recikliranje automobilskog materijala
[Wed Jul 30 14:05:19 2003]
Pavel Zamudio-Ramirez (1996) modeled part recovery and the materials recycling in the US auto industry to help the industry think about a future of enhanced auto recycling.
Pavel Zamudio-Ramirez (1996) oblikovao je obnavljanje dijelova i recikliranja materijala u američkoj automobilskoj industriji kako bi pomogao industriji da razmisli o budućnosti naglašenog recikliranja automobila.
[Wed Jul 30 14:08:25 2003]
Figure 619 shows a simplified stock and flow structure adapted from the model.
Slika 619 prikazuje pojednostavljenu strukturu stoka i toka prilagođenu modelu.
[Wed Jul 30 14:11:19 2003]
Old or wrecked cars can either be scrapped legally (sold to a junkyard or dismantler) or illegally abandoned.
Stari ili uništeni automobili mogu biti ili zakonski otpremljeni na otpad (prodani skladištu otpada ili rastavljaču dijelova) ili ilegalno napušteni.
[Wed Jul 30 14:11:48 2003]
The stock of abandoned, often burned-out, cars is a blight on the landscape and significant source of pollution.
Stok napuštenih, često zapaljenih, automobila je pogubno za krajolik i značajan je izvor zagađenja.
[Wed Jul 30 14:13:03 2003]
There are two outflows from the stock of illegally abandoned cars:
Postoje dva odljeva iz stoka ilegalno napuštenih automobila:
[Wed Jul 30 14:18:03 2003]
Dismantlers will process them if the value of the recoverable parts and materials is high enough.
Rastavljači dijelova će ih preraditi ako je vrijednost obnovljivih dijelova i materijali dovoljno visoka.
[Wed Jul 30 14:19:23 2003]
Alternatively, illegally dumped cars can be collected (say by local governments) and taken to shredders for proper disposal.
S druge strane, ilegalno odbačeni automobili mogu se sakupiti (npr. od strane lokalnih uprava) i otpremljeni na otpad u svrhu propisnog odlaganja.
[Wed Jul 30 14:19:23 2003]
Both these flows are relatively small, so the stock of abandoned cars can build up to high levels even if the abandonment rate is low
Oba ova toka su relativno mala, tako da stok napuštenih automobila može narasti na visok nivo čak i ako je stopa napuštanja niska
[Wed Jul 30 14:23:08 2003]
Cars held in the dismantlers' inventories are stripped of those parts whose value exceeds the cost of recovery.
Automobili koji se nalaze na otpadu lišeni su onih dijelova čija vrijednost premašuje cijenu obnavljanja.
[Wed Jul 30 14:23:29 2003]
These parts enter a used parts stock and are then sold to repair shops and used to replace worn or damaged parts on operating cars.
Ti dijelovi ulaze u stok rabljenih dijelova i prodaju se servisima radi zamjene istrošenih ili oštećenih dijelova na funkcionalnim automobilima.
[Wed Jul 30 14:25:02 2003]
In this map, the part usage rate flows into a sink.
Na ovoj mapi, stopa korištenja dijelova utječe u izljev.
[Wed Jul 30 14:26:40 2003]
In actuality, these parts are installed in cars still on the road and eventually flow again through the scrap or abandonment rate.
U stvarnosti, ovi dijelovi su ugrađeni u automobile koji su još na cesti i s vremenom opet prolaze kroz stopu otpada ili napuštanja.
[Wed Jul 30 14:26:40 2003]
Since the number of recovered parts is very small relative to the total flow of materials through the system, this omission is probably reasonable
S obzirom da je broj obnovljenih dijelova vrlo malen u usporedbi s ukupnim tokom materijala kroz sustav, ovo izostavljanje je vjerojatno opravdano
[Wed Jul 30 14:27:32 2003]
Stock and flow map for a model of automobile recycling
Mapa stoka i toka za model recikliranja automobila
[Wed Jul 30 14:35:40 2003]
The stock and flow structure for the development of new vehicle platforms, defining the mass and materials composition of cars and level of design for disassembly, is not shown The model includes a parallel stock and flow structure (co-flow) tracking each of these properties as vehicles age and are eventually retired dismantled and shredded See chapter 12
Struktura stoka i toka za razvoj novih platformi vozila, definiranje mase i strukture materijala automobila i stupanj oblikovanja za rastavljanje dijelova, nije prikazano Model uključuje paralelnu strukturu stoka i toka (paralelni tok) slijedeći svako od ovih svojstava kako vozila stare i s vremenom se otpremaju na otpad Vidi poglavlje 12
[Wed Jul 30 14:36:43 2003]
New Car Sales Rate
Stopa prodaje novih automobila
[Wed Jul 30 14:36:45 2003]
Cars on the Road
Automobili na cesti
[Wed Jul 30 14:36:50 2003]
Abandonment Rate
Stopa napuštanja
[Wed Jul 30 14:36:52 2003]
Abandoned Cars
Napušteni automobili
[Wed Jul 30 14:36:54 2003]
Scrap Rate
Stopa otpada
[Wed Jul 30 14:37:09 2003]
Part Usage Rate
Stopa korištenja dijelova
[Wed Jul 30 14:37:12 2003]
Used Parts Inventory
Zalihe rabljenih dijelova
[Wed Jul 30 14:37:31 2003]
Part Recovery Rate
Stopa obnavljanja dijelova
[Wed Jul 30 14:37:43 2003]
Dismantler Inventory
Inventar rastavljača dijelova
[Wed Jul 30 14:37:55 2003]
Dismantling Rate
Stopa rastavljanja
[Wed Jul 30 14:38:23 2003]
Abandoned Car Recovery Rate
Stopa obnavljanja napuštenih automobila
[Wed Jul 30 14:39:05 2003]
Dismantled Hulks
Rastavljeni trupovi automobila
[Wed Jul 30 14:39:39 2003]
Sales to Shredders
Prodaja auto-otpadu
[Wed Jul 30 14:41:39 2003]
Auto Materials in Landfills
Automobilski materijal na skladištima otpada
[Wed Jul 30 14:42:15 2003]
Disposal Rate
Stopa uklanjanja
[Wed Jul 30 14:42:38 2003]
Shredder Inventory
Inventar auto-otpada
[Wed Jul 30 14:43:17 2003]
Shredding Rate
Stopa uništavanja na auto-otpadu
[Wed Jul 30 14:43:26 2003]
Abandoned Car Disposal Rate
Stopa uklanjanja napuštenih automobila
[Wed Jul 30 14:43:43 2003]
Recyclable Materials
Reciklabilni materijali
[Wed Jul 30 14:43:56 2003]
Sales to Materials Processors
Prodaja prerađivačima materijala
[Wed Jul 30 14:43:58 2003]
Raw Materials Inventory
Inventar sirovina
[Wed Jul 30 14:43:58 2003]
Materials Usage Rate
Stopa korištenja materijala
[Wed Jul 30 14:48:58 2003]
After all parts worth recovering are removed, the gutted car, now called a hulk, is sold to a shredder.
Nakon uklanjanja svih dijelova koji se mogu obnoviti, tako "očišćen" automobil, tzv. trup automobila, prodaje se na auto-otpad.
[Wed Jul 30 14:49:39 2003]
In the mid 1990s there were about 200 shredders in the US who processed roughly 94% of all deregistered cars.
Sredinom 1990s postojalo je oko 200 auto-otpada u SAD-u koji su prerađivali otprilike 94 % svih automobila s odjavljenom registracijom.
[Wed Jul 30 14:52:22 2003]
After shredding, the valuable materials (principally steel and some nonferrous metals) are separated out for recycling.
Nakon uništavanja, vrijedni materijali (uglavnom čelik i neki obojeni metali) se odvajaju za recikliranje.
[Wed Jul 30 15:01:08 2003]
If the prices of the recovered materials don't justify the cost, shredders can take hulks directly to a landfill and cut their purchases from dismantlers.
Ako vrijednost obnovljenih materijala ne opravdava cijenu, auto-otpad može otpremiti trupove automobila direktno na skladište otpada i obustaviti njihovu kupnje od rastavljača dijelova.
[Wed Jul 30 15:02:58 2003]
What remains after shredding and separation is a mixture of plastics, glass, elastomers, and some unrecovered metal called automotive shredder residue (ASR) or "fluff," which is then landfilled.
Ono što ostane nakon uništavanja i odvajanja dijelova je mješavina plastike, stakla, elastomera, i nekih neobnovljenih metala, što nazivamo automobilski otpad nakon uništavanja (ASR - "automotive shredder residue") ili " staro željezo, " koje se zatim odvozi na skladište otpada.
[Wed Jul 30 15:02:58 2003]
ASR is one of the major environmental concerns generated by the disposal of old cars
ASR je jedan od glavnih ekoloških problema koji nastaje pored odlaganjem starih automobila
[Wed Jul 30 15:07:02 2003]
The recyclable materials accumulate in an inventory and are eventually sold to materials processors such as steel mills.
Preradivi materijali se gomilaju u zalihe i naposljetku se prodaju prerađivačima materijala, kao što su, na primjer, čeličane.
[Wed Jul 30 15:08:28 2003]
The inventory of raw materials is then used to manufacture new products, including automobiles, thus helping to create a closed material flow and cutting the use of nonrenewable resources.
Zalihe sirovina se tada koriste za izradu novih proizvoda, uključujući automobile, i na taj način pomažu stvaranje zatvorenog toka materijala, te smanjuju korištenje neobnovljivih izvora.
[Wed Jul 30 15:08:28 2003]
As in the case of parts, the materials usage rate flows into a sink since the flow of recovered materials relative to the total flow of virgin materials is small
Kao i u slučaju dijelova, stopa korištenja materijala utječe u izljev jer je tok obnovljenih materijala u odnosu na ukupan toku čistih materijala malen
[Wed Jul 30 15:11:24 2003]
Zamudio-Ramirez's model included a rich feedback structure representing the behavior of the various actors in the system, including the automakers, car owners, dismantlers, and shredders.
Zamudio-Ramirezov model uključuje bogatu povratnu strukturu prikazujući ponašanje različitih činilaca u sustavu, uključujući proizvođače automobila, vlasnike automobila, rastavljače dijelova, i auto-otpad.
[Wed Jul 30 15:13:41 2003]
Markets for recovered materials were explicit.
Tržišta za obnovljene materijale bila su jasna.
[Wed Jul 30 15:16:18 2003]
The stock and flow structure for autos began at the design stage for new models and platforms and tracked key properties of the cars including their mass, materials composition (ferrous, nonferrous, plastics), and the level of design for disassembly built into the design.
Struktura stoka i toka za aute započela je u fazi dizajniranja novih modela i platformi i slijedila je ključna svojstva automobila uključujući njihovu masu, sastav materijala (željezni, neželjezni, plastika), i razinu dizajna za rastavljanje uključeno u dizajn.
